We find certain special couplings for which the probability of the transmission between two given lines of the graph is strongly influenced by the potential applied on another line.
The new perspective is based on the well-known, but little exploited, relation between problem solving and the task of finding a path in a graph between two given nodes.
As a first step, we address the design of a single route, modeled as a path on a directed graph between two given nodes, maximizing a utility function related to the attractiveness of the path.
We use a modified version of Eppstein's k-shortest path algorithm (Eppstein, 1998), which efficiently computes the first k-shortest (or lightest) paths between two given nodes in a directed graph.
However, PPR is used for calculating the distance between two nodes in a given graph.
It captures not only the structure information about the query graph, but also implies strong connectivity constraints, i.e. the pairwise distance between any two given vertices.
Firstly, we give the following definitions of the order " (or )" between two graphs or two sets of graphs.
While general graphs can have multiple edges between two nodes, brain graphs tend to be simple graphs with a single undirected edge between pairs of nodes (i.e. the direction of influence between nodes is unknown).
A graph kernel calculates the similarity between two input graphs by comparing the relations between common vertices (nodes).
The semantic distance of UI method is 1 minus the percentage of overlapping nodes between two induced graphs among the total number of nodes in two graphs.
